In this paper, estimation of second order polynomial systems’ domain of attraction (DA) via rational Lyapunov function is investigated. One of the methods for estimating DA is to find the greatest level set. In this study, in order to obtain the greatest level set, cost function based on increasing the region enclosed to the level set has been offered instead of using shape factor.Estimating DA has been converted into solving bilinear matrix inequality optimization problem.Capacity of this method compared to other methods in recent studies has been shown through some examples.

This study aimed to estimate the genetic parameters of body weight traits in Markhoz goats, using B-spline random regression models. The data used in this study included 19549 records collected during 29 years (1992-2021) in Markhoz goat Breeding Research Station, located in Sanandaj, Iran. The model used to analyze data included fixed effects (year of birth, sex, type of birth and age of dam) and random effects including direct additive genetic, maternal additive genetic, permanent environmental and maternal permanent environmental assuming homogeneous and heterogeneous residual variance during the time. Akaike (BIC) and Bayesian (BIC) information criteria were used to compare the models and bspq.4.4.4.4 was selected as the best model. The direct heritability values for birth, 3-month, 6-month, 9-month and 12-month weights were estimated to be 0.14, 0.16, 0.08, 0.28 and 0.26, respectively. Genetic correlation between body weights at birth and 3-month, birth and 6-month, birth and 9-month, birth and 12-month, 3-month and 6-month, 3-month and 9-month, 3-month and 12-month, 6-months and 9-month and 9-month and 12-month were 0.22, 0.38, 0.21, 0.56, -0.26, 0.30, 0.62, 0.86 and 0.77, respectively. The highest phenotypic correlation was between the weight of 9-month and 12-month (0.82) and the lowest correlation was between birth weight and 3-month and 6-month (0.12). The results showed that the 9-month weight is a good criterion for selection in Markhoz goats.

In this paper, we are going to estimate the domain of attraction of tumor-free equilibrium points in a perturbed cancer tumor model describing the tumor-immune system competition dynamics. The proposed method is based on an optimization problem solution for a chosen Lyapunov function that can be casted in terms of Linear Matrix Inequalities constraint and Taylor expansion of nonlinear terms. We find a specific Lyapunov function in order to vanish maximum perturbation of modeling error, aging or uncertainties which exist in this system. Using this method and appropriate Lyapunov function, we demonstrate that there is an invariant polytope that for the set of perturbed initial conditions belonging to such region, the convergence to the healthy state is guaranteed.

In this article, an attempt has been made to estimate the amount of sound transmission loss in a flat oval channel by applying the approach of statistical energy analysis. Correct estimation of sound transmission loss in an air conditioning channel is of great importance due to the harmful effects of noise pollution in the environment on human health. Simulation with the statistical energy analysis method is a powerful approach to estimate sound and vibration in problems in which we deal with complex and multi-part systems; is considered. In this method, first, a system is divided into several subsystems, and then by writing a matrix equation that includes the energy exchanges between subsystems and energy loss coefficients; It is investigated from the perspective of vibration and sound estimation.On average, the model presented in this research is able to estimate the sound transmission loss in different dimensions of the air conditioning channels according to the experimental results in the accuracy range of ± 2.5 dB. Considering that it seems that the results obtained from modeling with this method are in good agreement with the experimental data; The results of this research can be used as an efficient approach to estimate noise in oval shaped channels stretched in different lengths.

In this work we use directional enlargement of domain of attraction to increase critical clearing time of nonlinear systems. To find the optimal control parameters, we use measure theory which converts the enlargement problem to a linear programming problem. At first step we find the critical directions of system, along them the system instability happens. After that we find optimal controlling parameters to extend domain of attraction along directions of interest. The efficiency of the proposed method is verified in simulation part for increasing critical clearing time of a power system with four machines.

Correct information about a power system’s dynamic variables is important and necessary for protection and control issues. Today's power systems, which differ from past systems, face new challenges due to converter-based resources. A solution to these challenges is dynamic state estimation in short time intervals, such as the time domain. This paper simulates a standard 68-bus system in the presence of converter-based resources with a high penetration percentage in DIgSILENT software and compares the performance of four Bayesian filters in estimating the dynamic variables of the synchronous generators of the system using values in the time domain with each other. The four types of filters used include extended Kalman filter, unscented Kalman filter, ensemble Kalman filter, and particle filter.The MATLAB software suite was used for the comparison of the performance of the four filter types in different scenarios, including the presence of measurement and processing noise, extreme noise, network fault, data missing, state estimation time by each filter, and the comparison of time domain method with other methods such as phasor domain. Finally, the advantages and disadvantages of each were identified.

The present study aimed to investigate the effect of domain-specific and domain-general precursors of mathematical training on preschoolers' number sense and estimation. This study adopted a quasi-experimental, pretest-posttest-follow-up design. The statistical population comprised all preschoolers in Kermanshah (Iran) in 2020. Using multi-stage cluster random sampling, a sample of 45 was selected and allocated to three groups (15 per group). The data were collected using the short form of the Wechsler Preschool and Primary Scale of Intelligence (WPPSI), the Number Sense Screener, and the PLUS test (number estimation). The data were analyzed using descriptive statistics and repeated-measures analysis of variance (ANOVA). The mean (SD) of IQ was 95. 91 (4. 21) in the working memory group and 97. 78 (3. 38) and 96. 66 (4. 03), respectively, in the number estimation and control groups. In the linear combination of number estimation variables in terms of group membership, the group x time interaction was significant on the pretest, posttest, and follow-up (p<0. 01). The difference in the mean scores of the working memory, number estimation, and control groups was also significant on the variable of number sense (p<0. 01). There was no significant difference in the effectiveness of the two training methods on the posttest and follow-up, and both interventions exerted the same effect on improving number sense and estimation.

The radon transform has a wide application in seismic processing for each project in different areas. Multiple attenuation is mostly summarized in the use of radon analysis in practice, especially in marine data processing. The definition of mute function is the major challenge in parabolic radon transform. In this paper, a method for segmentation of the radon transform by fuzzy inference system is introduced to separate energy parts in the radon domain. We applied a fuzzy inference system based on the property of energy distribution and its attribute in the radon domain. The result of clustering is the partitioning of the radon domain in three major classes: 1-random noise, 2-multiple, and 3-primary and multiple. The result of applying the new method on real data has shown the applicability of the new method for separation of multiple class from other classes that can assist the processor to define the mute function in the absence of other events in the radon domain